DNS Confusion

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I currently have a Hosting company X (Web and Email) and a DNS
Registration Company Y. For reference it's HostExcellence.com and
NetworkSolutions.com respectively.

The Regsistration Company sets the registration to Company X's DNS
servers and all is fine and dandy.

Now I want more control, want to learn and may migrate some hosting
deeds to my own servers.

So I change Registration Company Y DNS to point to Registration Company
Y's DNS Servers and start Editing the MX, A and CNAME records to point
to continue pointing at the same servers at Hosting Company X.

How is the DNS Server at the Hosting Company X know to remove/ignore
it's DNS Records for my domain. For example if I wish to point Email to
my own server and some user at Hosting Company X tries to send me
email, won't it use the Hosting Company X DNS server and route to the
old Email server?

Thanks